Linearly-polarized AIS Antennas
Artificial impedance surface antennas (AISAs) are realized by launching a surface wave across an artificial impedance surface (AIS), whose impedance is spatially modulated across the AIS according a function that matches the phase fronts between the surface wave on the AIS and the desired far-field radiation pattern.
In the prior art, an artificial impedance surface antenna (AISA) is formed from modulated artificial impedance surfaces (AIS). The prior art, in this regard, includes:
(1) Patel (see, for example, Patel, A. M.; Grbic, A., “A Printed Leaky-Wave Antenna Based on a Sinusoidally-Modulated Reactance Surface”, IEEE Transactions on Antennas and Propagation, vol. 59, no. 6, pp. 2087-2096, June 2011) demonstrated a scalar AISA using an endfire-flare-fed one-dimensional, spatially-modulated AIS consisting of a linear array of metallic strips on a grounded dielectric.
(2) Sievenpiper, Colbum and Fong (see, for example, D. Sievenpiper et al, “Holographic AISs for conformal antennas”, 29th Antennas Applications Symposium, 2005 & 2005 IEEE Antennas and Prop. Symp. Digest, vol. 1B, pp. 256-259, 2005; and B. Fong et al, “Scalar and Tensor Holographic Artificial Impedance Surfaces”, IEEE TAP., 58, 2010) have demonstrated scalar and tensor AISAs on both flat and curved surfaces using waveguide-fed or dipole-fed, two-dimensional, spatially-modulated AIS consisting of a grounded dielectric topped with a grid of metallic patches.
(3) Gregoire (see, for example, D. J. Gregoire and J. S. Colbum, “Artificial impedance surface antennas”, Proc. Antennas Appl. Symposium 2011, pp. 460-475; D. J. Gregoire and J. S. Colbum, “Artificial impedance surface antenna design and simulation”, Proc. Antennas Appl. Symposium 2010, pp. 288-303) has examined the dependence of AISA operation on its design properties.
The basic principle of AISA operation is to use the grid momentum of the modulated AIS to match the wavevector of an excited surface-wave front to a desired plane wave. In the one-dimensional case, this can be expressed asksw=ko sin θo−kp,  (Eqn. 1)where ko is the radiation's free-space wavenumber at the design frequency, θo is the angle of the desired radiation with respect to the AIS normal, kp=2π/p is the AIS grid momentum where p is the AIS modulation period, and ksw=noko is the surface wave's wavenumber, where no is the surface wave's refractive index averaged over the AIS modulation. The Surface Wave (SW) impedance is typically chosen to have a pattern that modulates the SW impedance sinusoidally along the Surface Wave Guide (SWG) according to the following equation:Z(x)=X+M cos(2π×/p)  (Eqn. 2)where p is the period of the modulation, X is the mean impedance, and M is the modulation amplitude. X, M and p are chosen such that the angle of the radiation θ in the x-z plane w.r.t the z axis is determined byθ=sin−1(n0−λ0/p)  (Eqn. 3)where n0 is the mean SW index and λ0 is the free-space wavelength of radiation. n0 is related to Z(x) by
      n    0    =                    1        p            ⁢                        ∫          0          p                ⁢                                            1              +                                                Z                  ⁡                                      (                    x                    )                                                  2                                              ⁢                                          ⁢          d          ⁢                                          ⁢          x                      ≈                            1          +                      X            2                              .      
The AISA impedance modulation of Eqn. 2 can be generalized for an AISA of any shape asZ({right arrow over (r)})=X+M cos(konor−{right arrow over (k)}o·{right arrow over (r)})where {right arrow over (k)}o is the desired radiation wave vector, {right arrow over (r)} is the three-dimensional position vector of the AIS, and r is the distance along the AIS from the surface-wave source to {right arrow over (r)} along a geodesic on the AIS surface. This expression can be used to determine the index modulation for an AISA of any geometry, flat, cylindrical, spherical, or any arbitrary shape. In some cases, determining the value of r is geometrically complex. For a flat AISA, it is simply r=√{square root over (x2+y2)}.
For a flat AISA designed to radiate into the wavevector at {right arrow over (k)}o=ko(sin θo{circumflex over (x)}+cos θo{circumflex over (z)}), with the surface-wave source located at x=y=0, the modulation function isZ(x,y)=X+M cos γwhere γ≡k0(n0r−x sin θ0).  (Eqn. 4)
The cos function in Eqn. 2 and Eqn. 3 can be replaced with any periodic function and the AISA will still operate as designed, but the details of the side lobes, bandwidth and beam squint will be affected.
The AIS can be realized as a grid of metallic patches disposed on a grounded dielectric that produces the desired index modulation by varying the size of the patches according to a function that correlates the patch size to the surface wave index. The correlation between index and patch size can be determined using simulations, calculation and/or measurement techniques. For example, Colburn and Fong (see references cited above) use a combination of HFSS unit-cell eigenvalue simulations and near field measurements of test boards to determine their correlation function. Fast approximate methods presented by Luukkonen (see, for example, O. Luukkonen et al, “Simple and accurate analytical model of planar grids and high-impedance surfaces comprising metal strips or patches”, IEEE Trans. Antennas Prop., vol. 56, 1624, 2008) can also be used to calculate the correlation. However, empirical correction factors are often applied to these methods. In many regimes, these methods agree very well with HFSS eigenvalue simulations and near-field measurements. They break down when the patch size is large compared to the substrate thickness, or when the surface-wave phase shift per unit cell approaches 180°.
Circularly-polarized AIS Antennas
An AIS antenna can be made to operate with circularly-polarized (CP) radiation by using an impedance surface whose impedance properties are anisotropic. Mathematically, the impedance is described at every point on the AIS by a tensor. In a generalization of the modulation function of equation (3) for the linear-polarized AISA [4], the impedance tensor of the CP AISA may have a form like
                              Z          =                      [                                                                                X                    -                                          M                      ⁢                                                                                          ⁢                      cos                      ⁢                                                                                          ⁢                      ϕ                      ⁢                                                                                          ⁢                      cos                      ⁢                                                                                          ⁢                      γ                                                                                                                                  1                      2                                        ⁢                    M                    ⁢                                                                                  ⁢                                          sin                      ⁡                                              (                                                  γ                          -                          ϕ                                                )                                                                                                                                                                                    1                      2                                        ⁢                    M                    ⁢                                                                                  ⁢                                          sin                      ⁡                                              (                                                  γ                          -                          ϕ                                                )                                                                                                                                  X                    +                                          M                      ⁢                                                                                          ⁢                      sin                      ⁢                                                                                          ⁢                      ϕ                      ⁢                                                                                          ⁢                      sin                      ⁢                                                                                          ⁢                      γ                                                                                            ]                          ;                            (                  Eqn          .                                          ⁢          5                )                                          where          ⁢                                          ⁢          tan          ⁢                                          ⁢          ϕ                ≡                              y            x                    .                                    (                  Eqn          .                                          ⁢          6                )            
In the article by B. Fong et al. identified above, the tensor impedance is realized with anisotropic metallic patches on a grounded dielectric substrate. The patches are squares of various sizes with a slice through the center of them. By varying the size of the patches and the angle of the slice through them, the desired tensor impedance of equation Eqn. 5 can be created across the entire AIS. Other types of tensor impedance elements besides the “sliced patch” can be used to create the tensor AIS.
Surface-wave Waveguide AIS Antennas
A variation on the AIS antennas utilizes surface-wave waveguides to confine the surface waves along narrow paths that form one-dimensional ES AISAs. Surface-wave waveguides (SWG) are surface structures that constrain surface-waves (SW) to propagate along a confined path (see, for example, D. J. Gregoire and A. V. Kabakian, “Surface-Wave Waveguides,” Antennas and Wireless Propagation Letters, IEEE, 10, 2011, pp. 1512-1515). In the simplest SWG, the structure interacts with surface waves in the same way that a fiber-optic transmission line interacts with light. The physical principle is the same: the wave preferentially propagates in a region of high refractive index surrounded by a region of low refractive index. In the case of the fiber optic, or any dielectric waveguide, the high- and low-index regions are realized with high and low-permittivity materials. In the case of the SWG, the high- and low-index regions can be realized with metallic patches of varying size and/or shape on a dielectric substrate.
The surface-wave fields across the width of the SWG are fairly uniform when the width of the SWG is less than approximately ¾ surface-wave wavelength. So, this is a good rule of thumb for the SWG.
In a linearly-polarized SWG AISA, the impedance of the SWG varies according to equation Eqn. 2. The impedance elements can be square patches of metal on the substrate or they can be strips that span the width of the SWG. The desired impedance modulation is created by varying the size of the impedance element dimensions with position.
In a circularly-polarized SWG, the tensor impedance varies according to equation Eqn. 5 with ϕ=0. The impedance elements can be the sliced patches as described by B. Fong et al. (see the B. Fong et al. article referenced above). The impedance element dimensions are varied with position to achieve the desired impedance variation.